Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2008-12-12
Nonlinear Sciences
Pattern Formation and Solitons
Scientific paper
10.1103/PhysRevE.78.066610
We consider a prototypical dynamical lattice model, namely, the discrete nonlinear Schroedinger equation on nonsquare lattice geometries. We present a systematic classification of the solutions that arise in principal six-lattice-site and three-lattice-site contours in the form of both discrete multipole solitons and discrete vortices. Additionally to identifying the possible states, we analytically track their linear stability both qualitatively and quantitatively. We find that among the six-site configurations, the hexapole of alternating phases, as well as the vortex of topological charge S=2 have intervals of stability; among three-site states, only the vortex of topological charge S=1 may be stable in the case of focusing nonlinearity. These conclusions are confirmed both for hexagonal and for honeycomb lattices by means of detailed numerical bifurcation analysis of the stationary states from the anticontinuum limit, and by direct simulations to monitor the dynamical instabilities, when the latter arise. The dynamics reveal a wealth of nonlinear behavior resulting not only in single-site solitary wave forms, but also in robust multisite breathing structures.
Bishop Alan R.
Frantzeskakis Dimitri J.
Kevrekidis Panagiotis G.
Koukouloyannis Vassilis
Kourakis Ioannis
No associations
LandOfFree
Discrete solitons and vortices in hexagonal and honeycomb lattices: Existence, stability, and dynamics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Discrete solitons and vortices in hexagonal and honeycomb lattices: Existence, stability, and dynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Discrete solitons and vortices in hexagonal and honeycomb lattices: Existence, stability, and dynamics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-609218